The gentle man who has written prior to my note is right on track. A couple of things come to mind, how large of a cart are you talking about and how heavy a load are needing to carry? I use pallet wood for everything. It is east to find and cheap. For a garbage wagon it would work great. I would make the sure the wheels are large cough so as to push or pull would be easy. If your using just a regular size garbage can, make the width at least 4 to 6 inches wider than the cans to aid it putting them in the cart. Also, Make it long enough to be able to turn with ease I would not think you would want to make the deck height higher than about 18 inches off the ground.
Any high lifting may be an issue. I would use 4 or 5 inch boards on the sides. space the side about 3 to 4 inches apart. At each corner use a couple of 2 x 4's set at 90 degree angles to each other. This will provide you a strong service to bolt your sides and end boards to. I would use bolts rather than screws to hold the boards in in place as screws will eventually allow the boards to come loose. Lay 2 x 4's along the bottom of your lowest side and end slat boards. These 2 x 4's, i would lay down with the narrow part of the 2 x 4's facing the pallet boards and the other side would face the inside of the wagon. Add one more 2 x 4 to middle of the wagon also on it's edge. Now you screw all of your bottom pallet boards to these three 2 x 4's. make one end of the wagon removable to get the cans in and out easily. I hope this may be of some help. I would use carriage type bolts on the side and end slats so as not to catch on everything, especially if you are moving in narrow spaces. Good Luck